Let `a_1, a_2, a_3, ?a_10 `are in G.P. if `a_3/a_1 =25` then `a_9/a_5` is equal to (A) `5^4` (B) `4.5^4` (C) `4.5^3` (D) `5^3`

Options

A. `2(5)^2`
B. `5^4`
C. `4(5^2)`
D. `5^3`

Answer

B

Explanation

For common ratio 'R'
`a_3/a_1 =25 rArr R^2 =25=5^2` …(1)
Hence `a_9/a_5=(a_1R^8)/(a_1R^4)=R^4 =(5^2)^2=5^4` {Using (1)}